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Considering the limitations of traditional Gaussian process regression in handling large datasets, this study employs multiple robots to explore the task area to gather environmental information and approximate the posterior distribution of the model using variational free energy methods, which serves as the input for the centroid Voronoi tessellation algorithm. Additionally, taking into consideration the localization errors, and the impact of obstacles, buffer factors and centroid Voronoi tessellation algorithms with separating hyperplanes are introduced for dynamic robot task area planning, ultimately achieving autonomous online decision-making and optimal coverage. Simulation results demonstrate that the proposed algorithm ensures the safety of multi-robot formations, exhibits higher iteration speed, and improves source localization accuracy, highlighting the effectiveness of model enhancements.<\/jats:p>","DOI":"10.1017\/s0263574725000050","type":"journal-article","created":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T21:16:39Z","timestamp":1747775799000},"page":"2100-2120","source":"Crossref","is-referenced-by-count":1,"title":["Multi-robot area coverage and source localization method based on variational sparse Gaussian process"],"prefix":"10.1017","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4972-108X","authenticated-orcid":false,"given":"Kai","family":"Cao","sequence":"first","affiliation":[{"name":"Xi\u2019an Technological University"},{"name":"University of California"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6519-4429","authenticated-orcid":false,"given":"Yunbo","family":"Wei","sequence":"additional","affiliation":[{"name":"Xi\u2019an Technological University"}]},{"given":"Yangquan","family":"Chen","sequence":"additional","affiliation":[{"name":"Xi\u2019an Technological University"},{"name":"University of California"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3483-5957","authenticated-orcid":false,"given":"Song","family":"Gao","sequence":"additional","affiliation":[{"name":"Xi\u2019an Technological University"}]},{"given":"Kun","family":"Yan","sequence":"additional","affiliation":[{"name":"Xi\u2019an Technological University"}]},{"given":"Shibo","family":"Yang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Technological University"}]}],"member":"56","published-online":{"date-parts":[[2025,5,21]]},"reference":[{"key":"S0263574725000050_ref12","doi-asserted-by":"publisher","DOI":"10.1109\/OJCS.2023.3238324"},{"key":"S0263574725000050_ref11","doi-asserted-by":"publisher","DOI":"10.20965\/jaciii.2022.p0342"},{"key":"S0263574725000050_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2021.107276"},{"key":"S0263574725000050_ref4","doi-asserted-by":"crossref","unstructured":"[4] Song, X. , Cheng, Y. , Qi, Q. and Zou, X. . \u201cA Path Planning Method for Robot-aided Aero-engine Ffeet Inspection Considering Resource Reuse Strategy.\u201d In: IEEE International Conference on Industrial Technology (ICIT) (2022) pp. 1\u20136.","DOI":"10.1109\/ICIT48603.2022.10002734"},{"key":"S0263574725000050_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2023.102570"},{"key":"S0263574725000050_ref30","unstructured":"[30] Luo, W. , Nam, C. , Kantor, G. and Sycara, K. . \u201cDistributed Environmental Modeling and Adaptive Sampling for Multi-robot Sensor Coverage.\u201d In: Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems (2019) pp. 1488\u20131496."},{"key":"S0263574725000050_ref23","doi-asserted-by":"crossref","unstructured":"[23] Ma, H. , Zhang, T. , Wu, Y. , Calmon, F. 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